Abstract
In this work, an analytic approach for solving higher order ordinary differential equations (ODEs) is developed. The techniques offer analytic flexibility in many research areas such as physics, engineering, and applied sciences and are effective for solving complex ODEs.
Highlights
The solutions of differential equations (DEs) are of much interest to engineers, physicists, mathematicians and researchers since many physical phenomena are modeled by using differential equations
We extend the concept of self-adjoint equations to solve higher order differential equations including odd orders, arguing that this work may serve as a reference for solving other higher order self-adjoint type ordinary differential equations (ODEs)
We provide two new analytic methods to solve some particular classes of higher order differential equations (ODEs), without the need of solving them numerically
Summary
The solutions of differential equations (DEs) are of much interest to engineers, physicists, mathematicians and researchers since many physical phenomena are modeled by using differential equations. In physics, Legendre DE [1], which is a self-adjoint ODE, arises in the solutions of Hydrogen atom wave functions and angular momentum in single-particle quantum mechanics. Their solutions form the polar angle part of the spherical harmonics basis for the multi pole expansion, which is used in both electromagnetic and gravitational statics. Solving higher order DEs is complex and numerical methods are usually needed to solve these equations with initial or boundary conditions. We provide two new analytic methods to solve some particular classes of higher order differential equations (ODEs), without the need of solving them numerically.
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